12 Laminate Thermoelastic Response The thermoelastic response of a general laminate may be very complex [1].For the particular case of unsymmetric laminates,bending-extension coupling, Equations (2.44)and (2.45)indicate the existence of out-of-plane deflections for a laminate subject to a temperature change.Hyer [2]and Dang and Hyer [3]have performed very detailed experiments and analysis of warping defor- mations of unsymmetric composite laminates during cooling from elevated (cure)temperatures.For symmetric laminates,however,it can be shown that the bending-extension coupling disappears,[B]=[0].For a balanced laminate,A=A26=0.Hence,a symmetric and balanced laminate behaves as a homogeneous orthotropic material in a macroscopic sense.Typical balanced symmetric laminates are [0/+45/90],[02/+45]3,and [02/902ls. For a symmetric and balanced laminate,Equation(2.51)yields 日& (12.1) where [NT]and [MT]are given by Equations (2.37)and(2.38).It may also be shown that the thermal moment resultants vanish,[MT]=[0],and the thermal in-plane shear force resultant N=0.Equations(12.1)then yield [e]=[A']N鬥 (12.2a) [K=[O (12.2b) Hence,a symmetric laminate does not bend due to a temperature change (Equation(12.2b)).The expanded form of Equation (12.2a)is N (12.3) 0 Consequently,Ysy=0,which shows that a balanced laminate will not deform in shear due to the temperature change. ©2003 by CRC Press LLC12 Laminate Thermoelastic Response The thermoelastic response of a general laminate may be very complex [1]. For the particular case of unsymmetric laminates, bending–extension coupling, Equations (2.44) and (2.45) indicate the existence of out-of-plane deflections for a laminate subject to a temperature change. Hyer [2] and Dang and Hyer [3] have performed very detailed experiments and analysis of warping defor￾mations of unsymmetric composite laminates during cooling from elevated (cure) temperatures. For symmetric laminates, however, it can be shown that the bending–extension coupling disappears, [B] = [0]. For a balanced laminate, A16 = A26 = 0. Hence, a symmetric and balanced laminate behaves as a homogeneous orthotropic material in a macroscopic sense. Typical balanced symmetric laminates are [0/±45/90]s, [02/±45]s, and [02/902]s. For a symmetric and balanced laminate, Equation (2.51) yields (12.1) where [NT] and [MT] are given by Equations (2.37) and (2.38). It may also be shown that the thermal moment resultants vanish, [MT] = [0], and the thermal in-plane shear force resultant = 0. Equations (12.1) then yield (12.2a) [κ] = [0] (12.2b) Hence, a symmetric laminate does not bend due to a temperature change (Equation (12.2b)). The expanded form of Equation (12.2a) is (12.3) Consequently, γxy = 0, which shows that a balanced laminate will not deform in shear due to the temperature change. ε κ o       = ′ ′       =       A D N M T T 0 0 Nxy T ε0 [ ] = [ ] A N ′ [ ] T ε ε γ x y xy x T y T A A A A A N N           = ′ ′ ′ ′ ′                     11 12 12 22 66 0 0 00 0 TX001_ch12_Frame Page 163 Saturday, September 21, 2002 5:05 AM © 2003 by CRC Press LLC